ME 405 Professor John M. Cimbala Lecture 30

Today, we will:

• Discuss Exhaust Duct System Design [Section 6.10] • Briefly discuss some additional considerations beyond ME 320 material • Show how to estimate major and minor head losses in ducts

Damper

Hood

Fan

Drop-out box

Q

Q

Equations for flow through ducts and pipes: Here is the head form of the steady-state, steady-flow (SSSF) energy equation for a control volume from an inlet (1) to an outlet (2) (from ME 320):

2 21 1 2 2

1 1 pump, 2 2 turbine,2 2u e LP V P Vz h z h hg g g g

α αρ ρ

+ + + = + + + +

Irreversible head losses: 2 2

,major ,minor 2 2L L L L

L V Vh h h f KD g g

= + = +∑ ∑ ∑ ∑

Minor Loss Coefficients for various entrances, elbows, and expansions: Note: We use KL as the minor loss coefficient in fluids class, but in HVAC we use C0. KL = C0.

loss coefficient C0 for round duct mounted in wall

t/D L/D 0.00 0.01 0.05 0.10 0.20 0.30 0.50 10.0

0.00 0.50 0.68 0.80 0.86 0.92 0.97 1.00 1.00 0.02 0.50 0.52 0.55 0.60 0.66 0.69 0.72 0.72 0.05 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 10.0 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

(a)

D (mm) 75 150 230 300 380 450 530 600 690 750 1500 C0, CD3-9 0.51 0.28 0.21 0.18 0.16 0.15 0.14 0.13 0.12 0.12 0.12 C0, CD3-10 0.16 0.12 0.10 0.08 0.07 0.06 - - 0.05 - 0.03

(b) Figure 6.29 Fitting loss coefficients: (a) duct mounted in a wall (also called a re-entrant inlet);

(b) round 90-degree elbows: 5 gore, r/D = 1.5 and 7 gore, r/D = 2.5 (abstracted from ASHRAE Fundamentals Handbook, 1997).

t

Q

L

D

ED1-1 duct mounted in

wall

Q

r

D

CD3-9 elbow 5 gore

90 degree r/D = 1.5

Q

r

D

CD3-10 elbow 7 gore

90 degree r/D = 2.5

loss coefficient C0 at listed values of A1/A0 and L/D0

A1/A0 L/D0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 12.0 14.0

1.5 0.03 0.03 0.04 0.05 0.06 0.08 0.10 0.11 0.13 2.0 0.04 0.04 0.04 0.05 0.05 0.06 0.08 0.09 0.10 2.5 0.06 0.06 0.06 0.06 0.06 0.06 0.07 0.08 0.09 3.0 0.09 0.07 0.07 0.06 0.06 0.07 0.07 0.08 0.08 4.0 0.12 0.10 0.09 0.08 0.08 0.08 0.08 0.08 0.08 6.0 0.16 0.13 0.12 0.10 0.10 0.09 0.09 0.09 0.08 8.0 0.18 0.15 0.13 0.12 0.11 0.10 0.09 0.09 0.09 10.0 0.20 0.16 0.14 0.13 0.12 0.11 0.10 0.09 0.09 20.0 0.24 0.20 0.17 0.15 0.14 0.12 0.11 0.11 0.10

optimum value of angle θ (degrees) at listed values of A1/A0 and L/D0

A1/A0 L/D0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 12.0 14.0

1.5 13 9 7 6 4 3 2 2 2 2.0 17 12 10 9 8 6 5 4 3 2.5 20 15 12 11 10 8 7 6 5 3.0 22 17 14 12 11 10 8 8 6 4.0 26 20 16 14 13 12 10 10 9 6.0 28 22 19 16 15 12 11 10 9 8.0 30 24 20 18 16 13 12 11 10 10.0 30 24 22 19 17 14 12 11 10 20.0 32 26 22 20 18 15 13 12 11

Figure 6.30 Fitting loss coefficients for an ED2-1 conical diffuser (abstracted from ASHRAE

Fundamentals Handbook, 1997).

Q

L

D0 θ H1

A1=H1W1

Q

A0=πD02/4

(round)

(rectangular)

ED2-1 conical diffuser round to plenum

Friction factor for major losses (losses in long straight sections of pipe or duct): Graphical estimate – the Moody Chart: [Figure from Cengel and Cimbala, Fluid Mechanics:

Fundamentals and Applications, Ed. 4.]

Empirical equation – the Churchill Equation: ( )1

12 121 588

Re.f A B − = + +

,

where 160 972 457 ln 0 27

Re

.

A . .Dε = − ⋅ +

,

1637530Re

B =

,

and f is the Darcy friction factor, 2

,major 2LL Vh fD g

= .

For non-circular ducts, use hydraulic diameter, 4 ch

ADp

= , where Ac is the cross-sectional

area of the duct and p is the wetted perimeter (always the entire perimeter for air flows).